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DOCUMENT RESUME
ED 081 309' HE 004 415
AUTHOR Cole, Nancy S.; Hanson, Gary R.TITLE Racial-EthniCBias in Selective College
Admission.PUB DATE 73NOTE 20p.; Paper prE,ented at American'Educational
Research Association 'Annual Meeting (New Orleans,Louisiana, 1973)
EDRS PRICE MF-$0.(- HC-$3.29DESCRIPTORS *Admission (School); *Admission Criteria, Bias; ,
College Admission; *Competitive Selection; HigherEducation; *Minority Groups; Negro Students;*Personnel Selection
ABSTRACTThe most commonly-,-used procedure in selective college
admissions involves selecting, students on the basis of predictedcollege grades computed from the regression of college grades on testscores and high school grades. Minority students have usually faredpoorly in the selective admissions process and, consequently, thepossibility of bias in.selective admission procedures is apparent.The authors examine the six different ideas of-bias in selection,analyze data from racial-ethnic minority students and majoritystudents from 35 colleges, and discuss the implications of theirstudy. The results indicate that models of bias with theoreticaldifferences yield practical differences when applied to selectkecollege admissions. The different value judgments the models enforceis of great importance,to: those implementing selection procedure\-since the choice of procedure in most cases diamatically affects thejudgments of fairness or bias. Colletge a.dmissionS personnel shouldgive consideration to the relation of selection procedures to the,values and goals of their colleges. (Author/PG)
, .1 j__FILMED FROM BEST AVAILABLE COPY
alACIAL2ET1tiNIC BIAS. IN SELECTIVE COLLEGE ADMISSIONS
-
t'uiliz?, .,-W-',f,
.
. .-ADften in the laSt_hundred yeairs higher education. in America has
. .
CP. played an important role in prOviding social and economic mobility or.\ t .
Nancy S. ColeGary'R.. Hanson
The AmeriCan College Testing program
I
relatively 'disadvantaged members of our society. /-To-day's disadvantaged
of primary concern-are members of racial7ethnic minorities, and again,CD
\
as in the past, higher education has assumed'a responSibility in attempting
to overcome some of the inequities suffered by these groups. A mar
thrust in this area has been achieved through the institUtion of special
programs for disadvantaged minority students at colleges across the nation.
However, in spite offrn.uch sympathy in many admissions, offices, minority
`...(-8tudens have usually 'fared poorly in the regular selective admissions1 / .. - .
.--, . . ..
.--process. 'Consequently, the possibilityof bias in selective admission
- procedures deserves careful:consideration.
The most commOnly-used.procedure in selective college admiSsions
involves selecting students cn th&basis of predicted college grades computed
from the regression of college gi.ades on.te.st scores and high -school grades.
Thus,' possible bias in these predi-Ctions (namely, systematic deviation of'
.predicted college grades from achieV' ed college' grades) has been thoroughly.
examined. Several authors reported that tests) were as predictive of college
grades in predominantly black colleges as in white colleges (Funches, 1967;
Hills & Stanley, .1970; Munday, 1965; Stanley & Porter, 1167). In studies
comparing blacks and whites in integrated colleg5s, the common resit
has been that, although t prediction equations may differ for the two'
groups, the use of prediOion equations based on all (or white) students
does not penalize blacks on the average and are often, in fact, biased in
their favor (Bowers, 1970; Cleary, 1968; Harris & Reitzel, ,1967; Kallingal,
1971; Pfeifer & Sedlacek, 1971; and Temp, 1971) . Thus., the conclusion
reached by many educators am.- explicated ,by Stanley (1'971). had been that
grade predictions are fair predictors of college succ.ess for minority students,
and rather than contributing to racial bias, such predictions indicate important
areas of educational disadvantage which must be recognized.4
Although grade predictions per se do not appear to be biased against
minority students, it does not follow that using grade predictions for selective
college admissions is in every way fair. Several authors have noted (e.g. Cole,
in press; Darlington, 1971; Thorndike, 1971) that there are many reasonable
definitions of bias; or its converse fairness, of which selection on the
basis of grade predictions under the regression approach is only one.
Cole (in press) examined six different ideas of bias in selection, each of
,which was shown to have different implications for the selection of minority
students in several hypothetical situations. The six models were the regression
models described above, the quota model, Darlington's subjective regressiori
model, the Einhorn-Bass equal risk model, Thorndike's constant ratio model,
and a-tosiditional probability, model.
Definitions 'of,Selection Bias
The regression model. When the regression model ofpredichons
is applied to selection situations, bias Is defined in terms of consistent
average errors of prediction. Thus, if (ao,,: , ap) denote the
r coefficients used to predict` college grades Y from p predictor variables.
(X4, , XP ),, then the difference betWeend mean predicted grades andP
/(,, mean observed grades will be indicated by r - y, where Y= a
xi+ Z a;x
, j 3x.
i
I
(/ An,indicator of the relatiVe bias in two groups, i and-j, under the regression..
model is then given.by BR
.
Y (yi - yj). (1)
When BR is positive, the prediction eq4ation is biased in favor of group i;
when negative, the bias is against grOup
3The quota model. Under the quota model of bias, the concern is
with proportional representation of difierentgroups among those Students
selected and involves the assignami of the desired representation a:priori.
Sex quotas are common it college adMission procedures, and racial-ethnic
quotas (such:as those which would 'match the proportional selection to the
propcNs
representation . in the lauer population) are 'sometimes, proposed7*
as fair in SelSctive college admiSsions.- A quota model involves a4 .
subjective judgment df the value of r4resentation of different groups
regardless of4redicted criterion scores or chances of success 'in college
and a procedure which meets the quotas is Judged fair.
The subjective regression model. Darlington (1911) proposed
a combination of the subjective' value judgments of the quota model with
the 'regression model by predicting. not the criterion alone but a weighted
combination of the criterion and some cultural variable. Thus, if onep (
ft'were willing to accept a minority student with a college grade of Y as
equal in subjective value...to- a majority student.with a grade)of. Y 10, then
the fair prOcedure would be to predic,t not Y but a function of Y, k, and C
(the cultural variable distinguishing Minority andim.ajority). Thus, 1.1. nder
this subjective regression model one proup.canqbe explicitly favored in the
selection process according to one's, subjective values, and the determination
of fairness or bias depends upon the subjective judgment made.
e ual-risk model. Under the equal .risk model (EinhOrn & Bass,
1971), fairness requires that. persons with equal chances of ,success on the
criterion be treated the same in selection. This model allows the selec*tor.-
111
to set a maximum level of risk to assume, and all applicants with
chances of success within the limit of risk are seledted regardless of
subgroup.
Bias according to the equal risk model occurs wheneVer the minimum
chance of success of those selected from one group differs from the minimum:
chance of those selected from another g-roup. In that case the se!ector's
risk would differ for the two groups. Thus, the indicator of bia4..computed
for this model is based op the maximum risk the selector takes in each group;
That risk for group i is
Pri{z < (Yp Yi) / .cry .x(i)
%h.
Vwhere Z is a unit,nurnial deviate, Y. is the predicted-grade cutofff
r-
for selection in group i, and is the criterion pass point. The
indicator of bias for groups i and j under the equal risk Ndel (BER)
is then given by
BER RISK (i) - RISK (j).-
4a
(2)
5.
The constant ratio model. Thorndike (1971) proposeTh:that in
a fair selection procedure the ratio of the proportion of 4 group selected.
(PrtY>Yil) to the proportion successful' Pr{Ys.Y0} should be the same1
for all groups when Y is the selection cutting4poiat and the criterion
pass point. Thus, an indictor: of bias under this model can be defined as
B CR
, P r >Y1}
Pi-p
Pr Ly>y2 }-2
Pr, {Y>Y IP
If BR is positive (the selection-success ratio is larger for group 11 than
for group 2), .then the bias favors group 1.a
The conditional probability model. Cole (in press) suggested that
the group most deserving fairness in many selection sithations is the group
of applicants who, if selected, would succeed. Under this model, selection
cutting points should be set so that the conditional probability of selectiL
given success in group i (Pri{Y>YilY>Yp}) is the same for each
racial-ethnic group. When applied to subsequent applicants, these cuttinga
points would assure eacli group of applicants the same chance of selection
among those who could succeed if selected. A Measure of bias under this
model isB
CP= Pr
1 {Y>Y1
1Y>Yp rP CM2 vY2 P
If BCP is positive the selection favois group 1 sVIce the conditional
probability is larger in group 1.
6
Comparison of models. The six. models, of bias are expressions
of different vaL,e' judgments applied to the .-.tlection situatio7,. Twc of the
models, the regression and equal 'risk models place strong positive value
on the selection'af highly successful students fo- college. Two other models',
the quota and subjective regiession models, place great value on the social
advantage of increased minority college enrollments regardless of other
concerns. The two'final models, the constant ratio and conditional probability
models, place greatest value on a fair/opportUnity for selection (as related'
to student' success) in all groups. The different implications of the six models
have been examined in several hypothethical situations by Cole (in press).
Some key differences are illustrated for oxe -t-y-pe of situation in,Figure 1
for the four statisticallybased models. From study of hypothetical situations
it is clear that the models can have dram tically different prescriptions
for how selection should be done. It is the purpose of this paper to examine
actual data from a Lumber of colleges, to determine to what extent present
selective admissions procedures are fair according to the ciofinitions
discussed.
Data
'Method',
Data from racial-ethnie min rity students_ (black or Mexican-American)
and majority students were analyzed \for 35 colleges. The colleges, sources
of the data, and size of minority and majority groups are described in Table 1.
The first 17 colleges listed in Table 1 were avatable from previously
published studies by Bowers (1970), Cleary (1968), & Reitzel.(1967),.
Pfeifer & Sedlacek (1971) and Tempi. (1971). The remaining 18 colleges
were drawn from the 1970, 1971, and 1972 Research Services of the American
College Testing Program (ACT). Ten'of, the colleges were rrbm the 1970 and 19-'1
Research Services through which those colleges identified black or Mexican-America
groups for special analys.es-. Student self-reported racial- ethnic identification was
available' in the 1972 Reseavch Services from regular adrnitiistration of the
ACT Assessment and eight integrated olleges with sufficient nutnbers of
minority students were analyzed.
The predictor" variables available arhong the 35 colleges included, .
high school rank and high. school grades, the Scholastic Aptitude Test (SAT)
cif the College Entrance Examination hoard, the'School and College Ability
Test, (SCAT), and`the ACT Assessment. In most cases the criterion was overall-,
first semester or first year "grade pbint average, but in the four cases
noted in Table 1 the' criterion was a first semester grade in a freshmanI
r--English course.
Procedure
-In selective college admissions, it iscomrnon for all racial-ethnic
groups to be combined for the construction of regression equations. Consequently,
this procedure was simulated in each of the. colleges studied, and the fair-d.
ness ,or bias in the procedure according to each definition of bias was examined.
When essentially all Minority and majority students .at a college were included .
The.authors acknowledge the kindness and helpfulness of Gedrge Temp,.
John B8wers,'"and Educational. Testing Strvice for providing the additional ,
information from Dr. Temp's study which was required for the "' aalyses..
in thelsamples available, the reyression enuation based on the total
sample was used. When the majority .group was sampled so that the .
\.
s,) \f---minority and majority ,samples were.- artificially of approximately equal
.. ,
size, the majority group regression equation was used to more nearly.n.
(approximate the equation for the total student body.
.Four the computation's of bias several additional assuMptions -we.re
Made. First, multivariate normality of triepredictors.and criterion was:
-
assumed. This 'assumption is commonly made and appears reasonable$
.in this type of data. Howeve.2, this -is not crucial to the models but ,a
convenience for computation. Second, a college grade pass point wasset.... ,..'.\
Because the grade scales varied grom college to- college, Y was set in. 1terms of the mean and standard deviation of the majority or combined
groupspecifically at one-half Standard devi-ation below the majority-or
combined mean, depending cn the particular samples analyzed. Since..:. ,,,
approximately 70%.of the students pass (or succeed) in college with this
value of Y it seemed a realistic choice for comparison of the mode4j".o
`-'7Vinall)r, to-compute b, specific prediCtor cutting point in each college, it
was necessary to specify what proportion of a?)plicants'came from each group and
what proportion of the, total applicants:could be accepted. because this information
was not available for the colleges being analyzer.:, the arbitrary assumption
2 dditional values of at the meau of the majority cornbinedgroup and one standard deviation below the mean,were examined for asample of the colleges and the results paralleled those presented here.
Is was made that 20% of the applicz.nts were from the minority group and
80% from the ma.jority.g'roup.E0r-each college. It was-further 0,ssurned! 0
that 50% of-the applicants could be se1(.(ted. thes.e figures were chosen
:o represent common College_admssions situations, but other values
also examined 'yielded esSentialiy results-
'.USing the computed regression equF)',,ons based on all available, 1 .
I t-,
prediCtors and the assumptiQnst note..1, forseach college the .neccessary- :,selection, cutting7pOint was '-:.impute l along with theindi.cators of bias defined
iri equations (I), (2), H) and (4 ). Althou'gh the bias indicators' as defined
are not in the same unit:,, they do seem to represent intuitively comparable
scales. In each case, zero represents no bias:, A bias as 'extreme as-
. 40, for 'example, represent a similarly large discrepancy in grade predictions
for -the- regression model-, in risk for the equal risk molel, in -selection-
success ratios for the fonstant ratio model, and in conditional probabilities--.for the conditto 1
I
probabiLity model. In addition, predictor-criterion' ',..
A ' ,.
correlations were computed for minority and majority groups within each'I
college as were ,the\proportion of (each group selected and the expectedI 4
,- })success rates of the,selectecl,groups (Pr. {y>y,,,jy>y. },1f:- . .i, P. I
-\ Results1
Level of Prediction
The median colrelation of predicted grade, based on all available\
:predictor variables, with-achieved grade was .34 for the minority groupe ,
3 The proportion of applicants from each group and proportion selectedwere varied in a sample' of colleges. For (minority, applicant proportion,majority appliCant proportion, and proportion selected), the additional valueseXamined were (:20,and (. 05, .95, :25), q.
75), (.20, .80, .25), (. 0.5, .95, .75), (.05, .95,. 60, . 75), (.40, .60, . 50), and (.40, . 60, .25)°.
.50),
4.(range: 02 to.. 67) and . 47. for thfrnajority grclup (range: .15 to ',. 72). .Fiy,
, . _,.cdntrase-the use _1'..searate within rkroup egrecsion equations reulted inp
, 4N ..\ .
'-median multiple correlations of .39'for the minority group and .49 fo the...
. .
majority group.
Selection Bias
The.distributions5 of.the bias indi:ators are given in Table-2. The .
,rise of a con -Wined prediction equation to selqct those students with the .
highest predieted grade's resulted n-7dest ov.erpredit-±tion of ,,:.racies in
the minority group ( Y - Y = C. 158) avid gt. very small.,underpreclit'tion. .\majority group (Y - - L-0.006). Thus, the moderate aVerdue hiaS (averag
BR 0. 16) faVors the minority group,according to the regression model-.
This result parallels the cC4.nrrion finding' that combined equations tend to
overf5rediet for m].\ority students. Note', however, that the use of separate
within grouji regression equations are by definition fair since the mean
piedicteil cr.i- terion (Y) and the criterion -mean (7) always coincide f6r
within
-
g'roup regression..
The risk in both groups was essentially the sameresUlting in an
avefage B 8R = 2. Thith, theiconibined regression procedure was fair
bOth groups according to the equal risk Model.
.-- '-`
° -4When test scores and high,
school. graci&s we.!:: analyzed separatelyfo1r the 18 colleges for which both were available, the Median multiplecorrelation. was.. 34 for tests and .34 for high school grades 'within the'minority. groups. For the majority groups the .corresponding figures were.43 for tests and .45 for high school grades. V,
The intermediate; results for each_college on which these dIE:!*.ite+_!tionsat4..based maybe' obtained- on rdquest from the authors.-
I Oa
HOWever, according to both the constant ratio and ccnditio,nal
probability models, the use of a combined predicticin equation and single
selection cutting ,point resulted in rather severe bias, on the average, against.
,minority ;students.: The average ratio of selection rates to succe-ss-rates
was -18 for the minority groui). and .80,for the majc.)1,?ty group indicating .
,that the Majority was selected, at a much higher rate in relation to their
success rate than were minority numbers. Similarly, the conditional
probability o`.. selection for potentially' successful minority,group members
vas only .31 while for majority group members this probability was .69.
eci"Thus, the averag.r.s_bias against the m inority group (a erag,e li c -. 3 2 ,
average 11.cp = -.34)--in the. use of a combined regre si-c7h equations isma.
extreme according to both the constant'ratib and ,cOnditional, probability
models.
Although bias indicators are not given for the subjeAtivo regression
and quota models,,f ome results are available. .Firrgii, the use of a combined
pred4ction equation resulted in an average regression favoritism for the
4
minority group which :might also be accomplished by using the
subjective regression model and a k value of'cbniparable inagnitude.
Second, in 33 of the 35 causes analyzedthe proportion of minority applicants
seletted was Considerably less than the proportion of majori!:y apple ants.selected. this results in proportional .minority 'representation in the
selected group of well less than the 2010 in the applicant group.
Success Rates ArrionestLes.
Selection via the cImbined prediction equatiop-,resulteci in an
average expected Success- rate of 64 among the minority students
selected and of .83 among selected majority students. Under 'inplication
of the regression Model. (use of separate equations) and equal risk model,
this discrepancy was sliglittly decreased. However,. use of either the
constant ratio or conditional probability models increased the dis'cr.ppancy
resulting in even lover minority expected sticce'ss 'rates.
Discussion
There are several important implications of the results of this
study. The results indicate that the models of bias with theoretical differences
yield practiCaldifferences as well when appliet,1 to the procesS of selective
college admissioi . As a consequence the discussion of the models and the
different value judgments they imp" _tment is of great practical importance
to those implementing selection procedures since the choice of procedure
in most cases dramatically affects the judgment of fairness or bias of the
procedure.
12
The correlations obtained shoNV the efficacy of test scores and high
school grades as predictors.in.niinority as well as Majority groups.._____ _ :
.
. ,..
,.although the corelations we're usually lower in the minoriFY group.
addition,' the depressing effect on the correlations.,un.de the'use of.a combined
prediction equatiOn rather than separate, Within group -equations is greatest
in the minority group. Thus, -when possible it i.s especially advantageous
to use ..'ithin minority group prediction equations.
Further, the results indicate that currently used cornbined equation
selection procedures fail to fit the definition of fairness given under the
regression, constant ratio, or conditional probability models. Under the
former, the minority group is favored while according to the latter two
bias against that group is indicated:* -Thus, whatever model's values arc.
C.-espou .ed, the -need for change is current procedures is :likely.
It should be noted that although the regression model of bias'is most
frequently favored in discussions of racial-ethnic bias, that model is rarely0
implemented in considerations of sex in selection. Hanson, _Cole, and Lamb
(in preparation) have shown that strict. use of the regression model for
selection of men And women would result in entering classeS- of two-thirds women
and one- third Yr-len. This unsatisfactory situation is apParently avoided by
most :idrnissions officers by accepting different..value judgments for the sex
selection situation -- ,namely quotas. One advantage of the conditional probability
modeis that it leads to socially meaningful results in cases both of sex
and racial-ethnic background, allowing a consistency in values across
both. It prescribes the selection of somewhat more minority students
13.
tha-a are now usually selected and also the selection of a fairly even
mix of men and women.
Finally, it is our-belief that college personnel implementing
selective college adMissions should give serious consideration to the
relation of selection procedti.res to the values appropriate to gdals. of
their colleges. We believe further that with such consideration many
colleges should Choose to implement the conditional ,probability model1
of fairness to guarantee equal opportunity of selection to potentially.successful students regardless of their rachial-ethnic background.
REFERENCES
Bowers, J. The comparison of CPA regression equations for regularly admittedand disadvantaged freshmen at the University of Illinois. Journal ofEducational Measurement, 1970, 7, 219 -225.
Cleary, T. A. Tosl?bias: Prediction of grades of negro and white studentsin int,egrittod colleges. .Journal of nducational NuaSnrement, 1968, 5,
115-124.
Cole, N. S. Mils in soIecti.oll. JOUrrld c) f i;ducitiunai :"Itilstirumen in pross.
. -
Darlington, R. IL Another look sit "culture fairness." Journal of Edt4rationalMeasurement, 1971, 8, 71.-82.
Einhorn, H. J., 6( Bass, A. R. Methodology considerations relevant to dis-crimination in employment testing. Psychological Bulletin, 1971,201.-269.
Fnnehes, 0. Correlations between secondary school transcript averages andgrade point averages and between ACT scores and grade point averages offreshmen at Jackson State College. Collejge and University, 1967, 43,52-54,
Harris, J., & Reitzel, J: Negro freshman performance a predominantly non-negrouniversity. The Journal of College Student. Personnel, 967, 8, .303-368.
J. R., & Stanley, J. C. Easier test improves vrediction of ne groescollege grades. Journal of Negor Education, 1970, 39,II 120-324.
Kailingal, A. The prediction of grades for black and white students atMichigan State University. Journal of Educational Measurement, 1971,,7, 219-225.
Munday, L. A. Predicting college grades in predominantly negro colleges.Journal of Educational Measurement, 1965, 2, 157-160.
Pfeifer, C.,M. Jr., 6, Sedlacek, W. E. The validity of academic predictors \
for black and white students-at a predominantly white university. Journal
of Educational Measurement, 1971, 8, 253-261.
Stanley, J. C. Predicting college success of the-educationally clsadvantaged.///Science, 1971, 171, 640-647.
Stanley, J. C., & Porter, A. C, Correlation of Scholastic Aptitude Test scorewith college grades for negroes versus whites. Journal of EducationalMeasurement, 1967, 4,.199 -218.
Temp,. C. .Validity of the SAT for blacks and whites in thirteen integt4itedcolleges. Journal of Educational Measurement, 1971, 8, 245-251.
Thorndike, R. L. ,Concepts of culture- fairness. Journal of EducationalMeasurement, 1971, 8, 63-70.
. 1.1.(;1?, I ( iN !l 0111,1-.
,
.C.; to ur:.
. PI i2dt: 6t
Gr.Itip I. \
°
REGRESSION MODEL: . Students with the highest, predicted GPAs, using separate equations.within groups, are selectedthe graph TIOVe',,:.:-.:tudeilf: in Group -1 with predictor
score X1 bas-the same,predicted'-GPA,as a student iM GT-,.."2 with predictor scoreThus_, While the model prescribes the selection of student'prdicted to'do,be,st-in.-CoTtege, the example illustrates the case inTwht-1,;_be.C.a-uerp,t-dic-L-ion is pooret in
.
one group (Group 2), Members of that'grdyp,Wi nign:predictoticOres must scorehigher than members'of another group to obtain the same predicted GPA.
l'A
1;.Q1.A I, RISK 2,101)1].
Group 1
.
l'ocs Point : ;
Group 2 RM. .
x 1 2
EQUAL RISK MODEL: Students with the highestchances of'sucCess orsmalles risk ate
selected Group 1 with.predictor score X1has the.samerisk as a student in Gr6UP 2
.
. .
with predictor s:7,te X2', Thus, while the model presCribes theselection of lowestrisk students,-;to.- example illustrates .the 'case in which because prediction is
poorer in onegroup (Group 2), members of that group withhigh predictor scores-must Score higher than members o f another 'group to have the same risk.
____
Fig. 1. 4 ,description and. contrast of four models of biaS.... .
c PA
i4,
C'ONSTAN'T RATIO .MOOV.),..
- Group I G!oup 2 .,,
A 1/.. 1B1
u
(NA Ai I 132/' I.1.,
' 1'P 1
Di !C :-1)2
I . 2Predctor Xi ) Pres. riutist ); 2
1
COSTSTANT RATIO-MODEL: Students are selected so that the ratio oseleced to proportion 'successful is the same in all groups.abbve an ellfpse of the' distribution of predictor and GPA score's
/ ;
;witn lqters which repregenl. the nUmber .of students falling, in Q
teas in the'graph. Thus, the propOrtion selected is representeand the proportion successful by (014-B)/(A+B.-K4-0),. K1 and X2 are
nonstant ratio model so that .4
0314-D)/(Ari-BD
Although . predict ion istwo modus; :X2 is less
members are successful-°-1 aid- very -few of the po
1
f he proportionIn -the graph
is presented along ,.
ach of the four'd by (B+D)/(A+B+C+D)
.set to satisfy the
poorer in Group 2 than Group 1, to the first.
than Xi. -However,. because a smaller proportion of.Group 2`Members of that grOup have a smaller . chalref zselection,:
te. tially ,:Successful -members of Group 2 are abOneg those
COND1TIONAL PROBA1311;11.1' NICOLL
Group 2
CPA A2 1 112
X
I
Prechrlor X2
CONDIDIONAL PROBABILITY MODEL; Stddents are selectif so,: that the conditionalprobability of selaCtion given success is the same for-all groups:. In the. ,
graph gbdve, :A4-13 representS. all successful. students snail therefore B/1(A+B)
represents the conditional Probability qf'fselec t on!,,giyen success . -X and XI 2
:are set to satisfy..'tbd';COfiditional probability- model So. rt-hat
- .. 13, / (A --i-B' ) a A(A,,-+-B4.-k 1 1 ':01' .2 h .4.
-. _
,, Q
As with-the' constant. ratio: although Pr0.dict4on is poorer in Group :2',, .. \ . '
X2 is lOss than ,l(i±HovieVOr,, ii1:::contrast_ to the other. three-models, the chances
of Selection:of. pOtentially,-Su essful_meMberS in both groups is.the-,sAme,.:..;indi'Cating.A. kind,of fairnes to t e whO.caft:succeed;'
G.
I
cted
TABLE 1
-Identification of Colleglus
Description of CollegeMinority Minority
Source of Data Group N
MajorityN PrediVtors"
A- Lastern,stAc :;upportcd Cleary(1968) Black 59 60 SAT-nsi,ern,tdte-,:upport.ed Cleary(1966) Black 83 36;,i SA1,HSRelthwestern,state.-supported Cleary(1968) Black 131 258 SAr,HSA
1) Univer:dty of 11linois Bowers(1970 SLOP 405' 4,855 SCAT,USPRPitt -,ipantly white rniversity Harris & Rvitzel(1967) Slack 45 3,895
i Tmp'..Colloge 1 Temp(1971) Black 100 100 SATTemp's Colle,,,;e 2 Temp(1971) Black 98 99 SATT4.,p' College 3 Temp(1911)
. Mack 104 104 SATI 4eAp's Co11,5ge 4 Temp(1971) Black 93 sAr
Tedp's College 5 . Temp(1971.) Black 140 140 Si',!
Temp's College 7 :n!... Temp(1971) Slack 99 100 SAT
1. 3gimp's College 3 Tc;Mp(197I) Black ]po 97 SAT
in Tmp's College 9, Temp(197I) Black 100 100 SATTemp's -College 10' Temp(1971) Black 100 95 SAL'
U I:mpis College 11 Tqpp(1971) Black 68 69 SATP "imp's Callegv 12 Teinp(1971)- Slack 39 100Q University of Miryland Pfeifer&Sedlacek(1971) Slack 126 178 .Ar-IsgsA
R Midwestern,state-upvori_ed
S
university umidwestern state-
1972 ACT Res. Serv. Nluck 131 2,653 Acr,wx,
supported university 1971 ACT Res. Serv. Slac-1: 130 4,97 Ac.I,HSG
T Large sonthru stateuniversity 1972 ACT Res. Serv. Illacc. 76 2,793 ACT,HSG
1.;') Aothern,state-supportd_
Vuniversity
f,outhern,stat.:-Iipported1971 ACT Res. Serv. Slack
Disad-146 . -1,335 ACI,111
university 1970'ACT Res. Serv. Vanta,ged 100 740 ACF,HSGW Southern,state-supported
university 1972 ACT Reg. Serv. Black 129 765 ACI,HSGX Sauthern,state-supported
university 1972 ACT Res. Serv. Black 117 1,073' ACT,HSGY Midwestern,state-supported
Aversily 1972 ACT. Res. Serv. Black 42 829 ACT,IISG
2 Large midwostern stateuniversity 1972 ACT/Res. Serv. Black 84 1,691 .ACT,HSG
AA Ea!:tern,privato college 1972 ACT Res. Sery Black 189 1,6')8
Eh !lidweuern state-supporteduniversity 1972 ACT Res. Serv. -Black 62 2,632 . ACT,HSG
CC Soutkrn,state-supported
buniversity 1.970 ACT Res: Serv. Black 260 1,987 ACT,IT;G
DD S.mthwestern,2-year college -1970 ACT Res: Serv. Chicano 108 170 'Ai-T,HSC.
EE SouChwestern,state-supported Spanishcollege 1970 ACT Res. Serv: surname 139 l 3 ACT,1156.
FF. Southwestern,state-supported 'Spanishcollege 1970 ACT Res. Serv. surname. 186 .1,155 ACT,iiSG
GG SoutWesiern,s,tate-supported Spanishuniversity 1970 ACT Res. Serv. surname' 105 147 ACT,HSG
III! Sonthwesterp,siat.e-supported Mexicanuniversity 1970 ACT Res. Serv. American 380 2,946 ACI,1156
Southwestern,state-supported Mexicanuniversity . 1970 ACT Res. Serv. American 369 . 748 AcrolsG
aSAT Scholastic Aptitude Test verbal and math scores; )ISR = high school rank in class;HSA = high school trade Average; SCAT a School and College Ability Test; IISRR = highschool percentile r'nk in class; ACT - 4 tests of the ACT Assessment; HSG = 4 student-reported 'high school grades.
The college grade Criterion Was the grade in a freshipan 'English ,course. In other C.11.!the criterion was first semestex or first year cone& grade point average.
TABLE 2
Distribution of Bias Indicators Using Majority or.Cdpbined Equationfor both the Majority and Minority Grdups
.40 or above
.20 to .39
.06 to .19
-.05 to .05'
-.19 to -.0.6.p_
'7:39 to -.20'.-..40.or.belour.,
Ave.
No, of Cases.'
.RegressionModelBR,
6
.9
-9
8
,
2
0 :-
1
.16
35
Equal Risk_ Model
BER
00
4
31:
0
0
0
.02
35'e/
Constant RatioModelBER
:2-0
..L
7
8
16
-.32
35
Conditional Prob.°Mbdel4CP. _
0
2
I
5
11
16
-.34
-35
Use FavorMinority
Use Fair
Use Unfair
to Minority
Exam
ination of Bias U
sing .Com
bined or MajorityR
egrscion: Equation
in Bdth M
inoritY-and M
ajority Ratial-E
thniups
College
Predictorsa
.f
Eqqationuseo
Moan
?redictn',..:lii:leC
o,rrel.azonsM
inus Observed
Standa.rd Errprs"of.F:s.tim
ateG
RA
!grIJm
iNR
.St
.E
Propor:inSelected
MIN
'M
AJ
,1.)
',..
ASA
T.
--44,4 ILI
.12.49',
.58.20
BSA
T,IiSR
,X
.,1.1,.04
0-40 3i...
.61.O
,.25
,..1, .67
.49.72
_39.
CSA
7,ESA
!.`,A2
790
.60.-,
.91..72
.47.75
D(m
en)- --SCA
3,OiSPR
:110'.
0,23
.37.41:
.68.02
--
D(t...om
en)-
-SCA
TO
-TSP8-----____M
'AJ
-.710
.23,
1.07,39....
.61.00
EIISR
,-' J ---------=
:,--_- -4-1-._.
-0' .50
.70.44
_58.70
F.
SAT
''
j!"1A3
.15-"----.21
.50.27.
.45.14
0SA
TM
A:-.1
,440
:-(Y5--:_-.--,--_,.__ :73' '
:22..53
25.
H.
SAT
MA
O.28
0.30
-
"76-2----'z.-:-.----,.:38.41
'.05
IM
AJ
.....210
..16.60
.33-----_--___, 49.05
JSA
TK
U17-
.37. 0
.45.68
'.55
.1-_____.qp
KSA
T. M
AJ
\..44
.0
.07_80 _
..15.
.69.05 ------:-
1.'' SA
TM
AJ
.020
..27.70
.51.76
.10M
., SA
TK
U.2.1
'0
.02.67
.45.49
.06N
.---=
,---1SAT
mA
J.47
.0
.34-.77
.25.44
.040
SAT
.M
AO
.040.
.08..55
..:42,'x;_
.1.9P
.. SA
TM
AJ
.0.0.--------.0"---T3:4-------.48,...
.49 '1'.56
'..13Q
(men)
SAT
,MSA
y.,1.,,,,-------.-.06.... '.00
.48:5,5
1:,7.-63--"-----...59.
.29b
Q..:om
en)SA
T,H
SA.
MA
O.30'
.62.64
".".65 :
.63---- 0R
.A
CT
;HSG
CO
MB
.00.00
.38.61
.58'.57
.04.00
-: .30S.
AC
T,H
,SG
-C
OM
B.12
.79.42
.66.
.07'T
AC
T,IiSG
CO
MB
"
.22-.01.
.48.68
.63'..64 ..
.31U
bA
CT
;11S0C
OM
B-.04
1
.00.26
"1.00..33
.93.40
.
V°
.A
CT
. HS G
.
,C
OM
B,
'...44
-.06 7:.67
"
- .86.70
-7'9.27
',,2A
C-I ,I1SO
CO
`C
O:.p3.
..30.-.05.
.43.72
.63'
.66.19
XA
C:.,-:::
- -CO
MB
.
'.11
-.01
.35...84
.62.73
..27
YA
C-I, H
SOC
1B....
-.01.17
.59.44
.62-.18
Z.
AC
T ,}{'SG
CO
MB
-45..02
.00.32
.62.40
..67.20
AA
Ati'i,titC
002.i-.03
..... .00"
:28.89 0.,
.43*.85
.19B
B:
Ai T
,HSG
CO
MB
--..20
-.04:37
-.57
i.55
'
.53.09.
'CC
AC
T.i!SG
CO
MB
.c",/ .23
- .0.3..
,-45.74 L
-58..77
.34E
D°
AC
T,H
SCC
O M
.3.10
-.05.09
,.76
.22..75.
230
EF.
AC
T,H
SCc0!-.11,
-.07.02'
.22'
.49.39-
.53.33
..
rFA
CT
,I1SG00'..',B
.05-.W
..' -.46.69
.53.67
.31G
Gb
AC
T H
SGC
OM
B..04
-.03 ;11'.49-
.89.59
.82.41"
?H
liA
CT
,H$G
".C
OM
B.21
-.03.51
.75,.50
.77.34
IIA
cT,H
SGco
-.13.06
.57.84
'..54
..74-.63
.57.52.64.61.62
-..,,.4
.T.*:
.56.61.61.-59.61
'159--.60.61.57.59:.55.54
1
.1
..6.54.52,..55-7
.55'.58
- .,P.57.60.53.56.
-.54.54.53'
.53.46
.32.28-.13.37.40.30.34.36.S9
..36.39 .
..34.32.38.40.33.30.25.29.31.34
Thorndike
;Cond.
C,ond. Prob. of
Risk
Ratio
of, SelectionSuccess
--I, (RA
JM
INm
A,J
.,qau
.29.31.27.28..30
' .29.29.31.
.32.27
.
.30.25-
'- .29.28.28.10
,32
.43.$2...,".,1.43
-82.68
:82Y
..29
11450.75
.:*45,.
.63.74
:83.19
1.53.64. -
.92
--
.59'
.50..92
".34.05
'.89',.:03
'
.70.68
,'.79
-----7-.33
.00
.89.
.00
.70.32j"
.78
.271.26.
..66
- .83H
:54.
.66.83
.32.35
.85'
.19'.64
.54-.76---------
..12
% .p1
.Sl
.27.60
..33
.75.33
-.27.88
.11.68
.40.78
'.33-
:17'.88
.07.67
.42i .77
.33.
3..86
.25_71
.47-.83
'.88
.06..64
.38,..,7S,
23..86
.15
.70.63
...82.23
:87'
.07.70
.29.80
...22
.88A
O -
.66.44
-.75.32
.38--:---...82.21
.56.
.55
'
.80 ..33
.25.85-
-.-19.69
:74 -'
AI
..19.-:.
.52
.79.41
----R.-88..1..._.79.
...87,.29
,80.79
.54.691--76-8----z__-., :87
.30.11
.85.08
-.73'
..73
-A.----
.31.170
.86.11..
...
:.69'
'.66
AO
.28, .62
-..78.45,9
'::68,.72
.87.30
.59.75
:46....,....Agf
.77.
...78
.25,:.
.65.76
.50 -'.---69
.:77
:91.2 7 .47
.77'.32
-.69 ," .67
.89'.2.
.49.78
.35.
.6s.
'
.72
.87.30.
.34'.82
.21.67
'.62
Al
.30 -:.35
.82.26
.65..74
.30.32
.81.24
.66.751
.8130..
.30.85
..17
.71'
.57 ..:,28
',62.75.
.47.65
Y.74- L
.87.30'
...."47
-
.76
.32
.60
- .67
.78.30
.45 ..,..79.36
.62.80
..79.28
,52,
.77.42
.65.80
.85.26'
.63::.74
...52.64
.83.88.
.
.28.
1.63'.75
'.48.63
..76
'
,.84 ,
.
.270
.83.73.
.73..59
.88A
B.
.32.33
a-SAT
=Scholastic Aptitude
Test.
verbal
and math scores;H
SR =
high school rank in'class;H
SAigh school grade average;
SCA
T -.School and -
College A
bility Test;
HSR
Rhigh' school percentile r nk in class;
AC
T =
4 tests of the AC
SAs
esszent; :HB
O =
'student.-reportea high. school:
griades.."
..
.
P
bThe college. grade criterion w
as the grade .1n4a freshman E
nglish course.'In other cases the crit+
-ion was first sem
ester,. or first year colleget
grade 'point average..
7